Approximation algorithms with constant ratio for general cluster routing problems

2021 ◽  
Author(s):  
Xiaoyan Zhang ◽  
Donglei Du ◽  
Gregory Gutin ◽  
Qiaoxia Ming ◽  
Jian Sun
Keyword(s):  
Approximation Algorithms ◽  
Constant Ratio ◽  
Routing Problems ◽  
General Cluster

Approximation Algorithms for Some Routing Problems

1978 ◽  
Vol 7 (2) ◽  
pp. 178-193 ◽  
Author(s):  
Greg N. Frederickson ◽  
Matthew S. Hecht ◽  
Chul E. Kim
Keyword(s):  
Approximation Algorithms ◽  
Routing Problems

MAXIMUM AREA INDEPENDENT SETS IN DISK INTERSECTION GRAPHS

2010 ◽  
Vol 20 (02) ◽  
pp. 105-118 ◽  
Author(s):  
SERGEY BEREG ◽  
ADRIAN DUMITRESCU ◽  
MINGHUI JIANG
Keyword(s):  
Combinatorial Optimization ◽  
Approximation Algorithms ◽  
Independent Set ◽  
Maximum Independent Set ◽  
Constant Ratio ◽  
Maximum Weight ◽  
Intersection Graphs ◽  
Maximum Area ◽  
Geometric Setting ◽  
Disk Area

Maximum Independent Set (MIS) and its relative Maximum Weight Independent Set (MWIS) are well-known problems in combinatorial optimization; they are NP-hard even in the geometric setting of unit disk graphs. In this paper, we study the Maximum Area Independent Set (MAIS) problem, a natural restricted version of MWIS in disk intersection graphs where the weight equals the disk area. We obtain: (i) Quantitative bounds on the maximum total area of an independent set relative to the union area; (ii) Practical constant-ratio approximation algorithms for finding an independent set with a large total area relative to the union area.

scholarly journals Approximation algorithms for some vehicle routing problems

2005 ◽  
Vol 146 (1) ◽  
pp. 27-42 ◽  
Author(s):  
Cristina Bazgan ◽  
Refael Hassin ◽  
Jérôme Monnot
Keyword(s):  
Approximation Algorithms ◽  
Vehicle Routing ◽  
Vehicle Routing Problems ◽  
Routing Problems

Constant Ratio Approximation Algorithms for the Rectangle Stabbing Problem and the Rectilinear Partitioning Problem

2002 ◽  
Vol 43 (1) ◽  
pp. 138-152 ◽  
Author(s):  
Daya Ram Gaur ◽  
Toshihide Ibaraki ◽  
Ramesh Krishnamurti
Keyword(s):  
Approximation Algorithms ◽  
Constant Ratio ◽  
Partitioning Problem

scholarly journals On the Performance of a Simple Approximation Algorithm for the Longest Path Problem

2019 ◽  
Vol 35 (1) ◽  
pp. 57-68
Author(s):  
Nguyen Thi Phuong ◽  
Tran Vinh Duc ◽  
Le Cong Thanh
Keyword(s):  
Approximation Algorithms ◽  
Approximation Algorithm ◽  
Polynomial Time ◽  
Undirected Graph ◽  
Simple Algorithm ◽  
Performance Ratio ◽  
Constant Ratio ◽  
Time Approximation ◽  
Longest Path ◽  
Longest Path Problem

The longest path problem is known to be NP-hard. Moreover, they cannot be approximated within a constant ratio, unless ${\rm P=NP}$. The best known polynomial time approximation algorithms for this problem essentially find a path of length that is the logarithm of the optimum.In this paper we investigate the performance of an approximation algorithm for this problem in almost every case. We show that a simple algorithm, based on depth-first search, finds on almost every undirected graph $G=(V,E)$ a path of length more than $|V|-3\sqrt{|V| \log |V|}$ and so has performance ratio less than $1+4\sqrt{\log |V|/|V|}$.\

scholarly journals Better Approximation Algorithms for Grasp-and-Delivery Robot Routing Problems

2013 ◽  
Vol E96.D (3) ◽  
pp. 450-456 ◽  
Author(s):  
Aleksandar SHURBEVSKI ◽  
Hiroshi NAGAMOCHI ◽  
Yoshiyuki KARUNO
Keyword(s):  
Approximation Algorithms ◽  
Routing Problems
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